Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia `3.30kg*m^(2)` about its central axis, is set spinning counterclockwise at 450 rev/min. The second disk, with rotational inertia `6.60 kg*m^(2)` about its central axis, is set spinning counterclockwise at 900 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 900 rev/min, what are their (b) angular speed and (c ) direction of rotation after they couple together?

Explanation

To solve the problem step by step, we will use the principle of conservation of angular momentum.

### Step-by-Step Solution

**Step 1: Understand the System and Given Data**
- We have two disks with the following properties:
- Disk 1:
- Rotational Inertia \( I_1 = 3.30 \, \text{kg} \cdot \text{m}^2 \)
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